13. permeability properties

7/24/2019 13. Permeability Properties

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13Because o their low density, polymers are relatively permeable to gases and liq-

uids. A more in-depth knowledge o permeability is necessary when dealing with

packaging applications and with protection coatings or corrosive environments.

The material transport o gases and liquids through polymers consists o various

steps. They are:

Absorption o the diffusing material at the interace o the polymer, a process

also known as adsorption,

Diffusion o the attacking medium through the polymer, and

Delivery or secretion o the diffused material through the polymer interace, also

known as desorption.

With polymeric materials these processes can occur only i the ollowing rules areulfilled:

The molecules o the permeating materials are inert,

The polymer represents a homogeneous continuum, and

The polymer has no cracks or voids that can channel the permeating material.

In practical cases, such conditions are ofen not present. Nevertheless, this chapter

shall start with these ideal cases, because they allow or useul estimates and

serve as learning tools or these processes.

13.1Sorption

We talk about adsorption when environmental materials are deposited on the sur-

ace o solids. Interace orces retain colliding molecules or a certain time. Possi-

ble causes include van der Waals orces in the case o physical adsorption,

chemical affinity (chemical sorption), or electrostatic orces. With polymers, wehave to take into account all o these possibilities.

Permeability Propertiesof Polymers


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13Permeability Properties of Polymers

A gradient in concentration o the permeating substance inside the material

results in a transport o that substance which we call molecular diffusion. The

cause o molecular diffusion is the thermal motion o molecules that permit the

oreign molecule to move along the concentration gradient using the intermolecu-

lar and intramolecular spaces. However, the possibility to migrate essentiallydepends on the size o the migrating molecule.

The rate o permeation or the case shown schematically in Fig. 13.1 is defined as

the mass o penetrating gas or liquid that passes through a polymer membrane per

unit time. The rate o permeation, m , can be defined using Ficks first law o diffu-

sion as

m DA dc

dx=

(13.1)

whereDis defined as the diffusion coefficient, Ais the area, and the density. Ithe diffusion coefficient is constant, Eq. 13.1 can be easily integrated to give

m DA c c L= ( ) 1 2 / (13.2)

The equilibrium concentrations c1and c2can be calculated using the pressure, p,

and the sorption equilibrium parameter, S:

c Sp= (13.3)

which is ofen reerred to asHenrys law.

p2, c

2p

1, c

1Polymer

x = 0 x = L

m

Figure 13.1Schematic diagram of

permeability through a film

The sorption equilibrium constant, also reerred to as solubility constant, is almost

the same or all polymer materials. However, it does depend largely on the type o

gas and on the boiling temperature, Tb, or the critical temperature, Tcr, o the gas,

such as shown in Fig. 13.2.


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. Diffusion and Permeation

13.2Diffusion and Permeation

Diffusion, however, is only one part o permeation. First, the permeating substance

has to infiltrate the surace o the membrane; it has to be absorbed by the mem-

brane. Similarly, the permeating substance has to be desorbed on the opposite side

o the membrane. Combining Eq. 13.2 and 13.3 we can calculate the sorption

equilibrium using

m DS A p p L= ( ) 1 2 / (13.4)

where the product o the sorption equilibrium parameter and the diffusion coeffi-

cient is defined as thepermeabilityo a material

P DS mL

A p= =

(13.5)

Equation 13.5 does not take into account the influence o pressure on the permea-

bility o the material and is only valid or dilute solutions. The Henry-Langmuir

modeltakes into account the influence o pressure and works very well or amor-

phous thermoplastics. It is written as

P DS KR

b p

= ++

11

(13.6)

where K c b SH= / , with cH being a saturation capacity constant and b an affinity

coefficient. The constant R represents the degree o mobility, R= 0 or complete

0

0.01

0.1

1

cm3/cm3

Solubility

10

100 200

Temperature, T

300 K 400

O2

N2

N2

O2

CH4

C2H

4

C4H

6

Tb

C4H

10

SO2

C2H

6

NH3

CO2

H2

CH4

CO2

C2H

6

NH3

C4H

10

SO2

Tcr

log S(298) = -2.1 + 0.0123 Tb

Figure 13.2Solubility

(cm3/cm3) of gas in natural

rubber at 25 C and 1 bar as a

function of the critical and the

boiling temperatures


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immobility and R= 1 or total mobility. Table 13.1 [1] presents permeability o var-

ious gases at room temperature through several polymer films. In the case o multi-

layered films commonly used as packaging material, we can calculate the

permeation coefficientPC or the composite membrane using

1 11

P L

L

PC Ci

i n i

i

= ==

(13.7)

Table 13.1 Permeability of Various Gases through Several Polymer Films

Permeability (cm3mil/100 in2/24 h/atm)

Polymer CO2 O2 H2O

PET 1220 510 24

OPET 6 3 1PVC 4.7540 815 23

HDPE 300 100 0.5

LDPE 425 11.5

PP 450 150 0.5

EVOH 0.050.4 0.050.2 15

PVDC 1 0.15 0.1

Sorption, diffusion, and permeation are processes activated by heat and, asexpected, ollow an Arrhenius type behavior. Thus, we can write

S S e H RT

s=

0

/ (13.8)

D D e E RT

D=

0

/and (13.9)

P P e P RTE

=

0

/ (13.10)

whereH

S

is the enthalpy o sorption, EDand Epare diffusion and permeation acti-vation energies,Ris the ideal gas constant, and Tis the absolute temperature. The

Arrhenius behavior o sorption, diffusion, and permeability coefficients as a unc-

tion o temperature or polyethylene and methyl bromine at 600 mm o Hg is shown

in Fig. 13.3 [2]. Figure 13.4 [3] presents the permeability o water vapor through

several polymers as a unction o temperature. It should be noted that permeability

properties drastically change once the temperature exceeds the glass transition

temperature. This is demonstrated in Table 13.2 [4], which presents Arrhenius

constants or diffusion o selected polymers and CH3OH.

The diffusion activation energyEDdepends on the temperature, the size o the gas

molecule dx, and the glass transition temperature o the polymer. This relationship

is well represented in Fig. 13.5 [1] with the size o nitrogen molecules, dN2 as a


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2.3

2.9 3.1 3.3 3.5 3.7 3.9

2.5

2.7

2.9

log

scale

3.1

3.3

3.5

3.7

3.9

103

T

D*1010

P*1010

S*1010

Figure 13.3Sorption, diffusion,

and permeability coefficients, as a

function of temperature for poly-

ethylene and methyl bromine at

600 mm of Hg

3.010-8

10-7

10-6

cm2/(bar*s)

10-5

3.2 10-3*1/K

Inverse temperature, 1/T

Permeability,

P

3.6

Rubber-hydrochloride

Polyvinylidene-chloride

Polyethylene

Poly vinylchloride

Vinyl chloride/Vinyl acetate copol.

Polystyrene

Figure 13.4Permeability ofwater vapor as a function of

temperature through various

polymer films


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reerence. Table 13.2 contains values o the effective cross section size o impor-

tant gas molecules. Using Fig. 13.5 with the values rom Table 13.1 and using the

equations presented in Table 13.3, the diffusion coefficient,D, or several polymers

and gases can be calculated.

Table 13.4 also demonstrates that permeability properties are dependent on thedegree o crystallinity. Figure 13.6 presents the permeability o polyethylene films

o different densities as a unction o temperature. Again, the Arrhenius relation

becomes evident.

Table 13.2 Diffusion Constants Below and Above the Glass Transition Temperature

Polymer Tg(C) D0(cm2/s) ED(Kcal/mol)

T < Tg T > Tg T < Tg T > Tg

Polymethylmethacrylate 90 0.37 110 12.4 21.6

Polystyrene 88 0.33 37 9.7 17.5

Polyvinyl acetate 30 0.02 300 7.6 20.5

Glass transition temperature, Tg

0

100 200 300 400 50020 40 60 80 20 40 60 8 0 20 40 60 80 20 40 60 8 0 20

1

2 18

19

20

8

3 21

5

6

7

22

10

12

1411

13

24

2315

16

17

25

4

1

2

3

4

5

6

7

8

9

26

dN2

EDR

dx

2

Figure 13.5 Graph to determine the diffusion activation energy EDas a function of glasstransition temperature and size of the gas molecule dx, using the size of a nitrogen molecule,

dN2, as a reference.

Rubbery polymers ( ): 1 = Silicone rubber, 2 = Polybutadiene, 3 = Natural rubber,

4 = Butadiene/acrylonitrile (80/20), 5 = Butadiene/acrylonitrile (73/27), 6 = Butadiene/

acrylonitrile (68/32), 7 = Butadiene/acrylonitrile (61/39), 8 = Butyl rubber, 9 = Polyurethane

rubber, 10 = Polyvinyl acetate, 11= Polyethylene terephthalate.

Glassy polymers ( ): 12 = Polyvinyl acetate, 13 = Vinyl chloride/vinyl acetate copolymer,

14 = Polyvinyl chloride, 15 = Polymethyl methacrylate, 16 = Polystyrene, 17 = Polycarbonate.

Semi-crystalline polymers (x): 18 = High-density polyethylene, 19 = Low density polyethylene,

20 = Polymethylene oxide, 21 = Gutta percha, 22 = Polypropylene, 23 = Polychlorotrifluoro-ethylene, 24 = Polyethylene terephthalate, 25 = Polytetrafluoro ethylene, 26 = Poly(2,6-diphe-

nylphenylene oxide).


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Table 13.3 Important Properties of Gases

Gas d Vcr Tb Tcr dN2/dx

(nm) (cm3) (K) (K)

He 0.255 58 4.3 5.3 0.67

H2O 0.370 56 373 647 0.97

H2 0.282 65 20 33 0.74

Ne 0.282 42 27 44.5 0.74

NH3 0.290 72.5 240 406 0.76

O2 0.347 74 90 55 0.91

Ar 0.354 75 87.5 151 0.93

CH3OH 0.363 118 338 513 0.96

Kr 0.366 92 121 209 0.96

CO 0.369 93 82 133 0.97

CH4 0.376 99.5 112 191 0.99

N2 0.380 90 77 126 1.00

CO2 0.380 94 195 304 1.00

Xe 0.405 119 164 290 1.06

SO2 0.411 122 263 431 1.08

C2H4 0.416 124 175 283 1.09

CH3Cl 0.418 143 249 416 1.10

C2H6 0.444 148 185 305 1.17

CH2Cl2 0.490 193 313 510 1.28

C3H8 0.512 200 231 370 1.34

C6H6 0.535 260 353 562 1.41

Table 13.4 Equations to Compute DUsing Data from Table 13.1 and Table 13.2 a

ElastomersDlog 4D

E

2.3R

1

T

1

DT

=

Amorphous thermoplasticsDlog 5D

E

2.3R

1

T

1

DT

=

Semi-crystalline thermoplasticsDlog 5D

E

2.3R

1

T

1

DT

= x1

aTR= K and X is the degree of crystallinity.


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13.3Measuring S, D, and P

ThepermeabilityPo a gas through a polymer can be measured directly by deter-

mining the transport o mass through a membrane per unit time.

The sorption constant S can be measured by placing a saturated sample into an

environment that allows the sample to desorb and measure the loss o weight. As

shown in Fig. 13.7, it is common to plot the ratio o concentration o absorbed sub-

stance c(t) to saturation coefficient cwith respect to the root o time.

2.8

10-9

10-8

cm2/(bar*s)

10-7

3.0 3.2

Inverse temperature, 1/T

Permeability,

P

3.610-3K-1

= 0.932

0.938

0.9540.96

Figure 13.6Permeation of nitrogen

through polyethylene films of various

densities

a

ts

t

c(t)

c

Figure 13.7Schematic diagram of

sorption as a function time


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TheDiffusion coefficient is determined using sorption curves as the one shown in

Fig. 13.7. Using the slope o the curve, , we can compute the diffusion coefficient

as

D L a=

16

2 2

(13.11)

whereLis the thickness o the membrane.

Another method uses the lag time, t0, rom the beginning o the permeation pro-

cess until the equilibrium permeation has occurred, as shown in Fig. 13.8. Here,

the diffusion coefficient is calculated using

D L

t=

2

06

(13.12)

The most important techniques used to determine gas permeability o polymers

are the ISO 2556, DIN 53 380, and ASTM D 1434 standard tests.

13.4Corrosion of Polymers and Cracking [5]

In contrast to metallic corrosion, where electrochemical corrosion mechanisms aredominant, several mechanisms play a role in the degradation o polymers. Attacks

may occur by physical or chemical means or by a combination o both.

Even without a chemical reaction, the purely physical effect o a surrounding

medium can adversely affect the properties o a polymer. Due to the low density o

polymers, every surrounding medium that has moveable molecules will infiltrate

or permeate the polymer. Experiments have shown that polymer samples under

high hydrostatic pressures have even been permeated by silicone oils, which are

completely inert at low pressures. The infiltration o silicone oil caused stress

cracks and embrittlement in amorphous thermoplastics in the regions o low den-

sity, such as particle boundaries, filler material interaces, and general surace

imperections. I we consider imperections or particles o characteristic sizeL, we

t=0

m

t0

t

Transientdiffusion

Steady statediffusion

Figure 13.8Schematic diagram of diffusion as

a function of time

. Corrosion of Polymers and Cracking


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can perorm an energy balance and conclude that the critical strain, crit

, at which

a crack will occur is given by [6]

crit~

EL (13.13)

where E represents Youngs modulus and the adhesion tension between the

individual particles. Crack ormation and propagation is shown schematically in

Fig. 13.9 [7]. Figure 13.101shows an electron micrograph o a medium permeating

through the inter-spherulitic boundaries o polypropylene.

Figure 13.9 Schematic diagram of crack formation and propagation during diffusion

Desorption, schematically shown in Fig. 13.11, is also undesirable or polymeric

components. Similar to soil, which cracks as it dries out too quickly, the stressesthat arise as the medium desorbs rom the polymer give rise to cracks that may

lead to ailure o the component. As the absorbed medium desorbs, the polymer

component shrinks according to the loss o volume. However, inner layers that

remain saturated do not shrink, leading to residual stress build-up similar to that

occurring with a cooling component with high temperature gradients. The sche-

matic o the residual stress build-up and concentration o the absorbed medium is

shown in Fig. 13.12 [8]. The stress history at the edge and center o a desorbing

film is shown in Fig. 13.13. The stresses that arise during desorption are easily

three times larger than during absorption. The maximum stress that occurs at theouter edge o the part can be calculated using

max saturation

=

E

v1 (13.14)

The volume change in the immediate surace o the component is caused by the

desorption process. Auxiliary agents or processing, such as coloring agents, so-

teners, stabilizers, and lubricants, as well as low molecular components o the

polymer, may act as desorption agents.

1 Courtesy IKV Aachen.


11/12

Figure 13.10Electron micro-

graph of permeating medium

through the inter-spherulitic

boundaries of polypropylene

Figure 13.11Schematic

diagram of desorption from a

plateL

Figure 13.12 Schematic concentration ( C) and residual stress R( )as function of time inside

a plate during desorption

t0

t1

t2

t3

t4

t5

t0

t1

t2

t3

t4

t5

Undesirable situation

Residualstress

Concentration

R

C

. Corrosion of Polymers and Cracking


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13.5Diffusion of Polymer Molecules and

Self-diffusion

The ability to infiltrate the surace o a host material decreases with molecular

size. Molecules oM> 5 10 3can hardly diffuse through a porous-ree membrane.

Sel-diffusion is when a molecule moves, say in the melt, during crystallization.

Also, when bonding rubber, the so-called tack is explained by the sel-diffusion o

the molecules. The diffusion coefficient or sel-diffusion is o the order o

D

T

~ (13.15)

where Tis the temperature and the viscosity o the melt.

References

[1] Rosato, D., and Rosato, D. V., Blow Molding Handbook, Hanser Publishers, Munich,

(2003).

[2] Rogers, C. E.,Engineering Design for Plastics,Ed. E. Baer, Chapter 9, Robert E. Krieger

Publishing Company, Huntington, (1975).

[3] Knappe, W., VDI-Berichte, 68, 29, (1963).

[4] Van Krevelen, D. W,Properties of Polymers, 4th ed., Elsevier, Amsterdam, (2009)

[5] Menges, G., and Lwer, K., Metallic Corrosion: Proceedings, 8th ICMC, 2202, Mainz

(1981).

[6] Menges, G.,Kunststoffe, 63, 95, (1973).

[7] Menges, G. and Suchanek, H., Kunststoffe, Fortschrittsberichte, Vol. 3, Hanser Pub-

lishers, Munich, (1976).

[8] Ptz, D., Ph. D. Thesis, IKV, RWTH-Aachen, Germany, (1977).

t1

Q

t0

t1

t1 x = 0

x = L/2

Compressive

Tensile

Stress

t1

t1

log t

Figure 13.13Residual stresses

inside a plate during desorption
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